Circular vertex arboricity

The vertex arboricity va(G)va(G) of graph GG is defined as the minimum of subsets in a partition of the vertex set of GG so that each subset induces an acyclic subgraph and has been widely studied. We define the concept of circular vertex arboricity vac(G)vac(G) of graph GG, which is a natural generalization of vertex arboricity. We give some basic properties of circular vertex arboricity and study the circular vertex arboricity of planar graphs.